I don't know about the DS, but I have a friend whose kid jacked up his Gameboy SP and asked me if I knew how to get them fixed. After a little research, I found that replacing the LCD is essentially impossible or at best impractical.
As a last-ditch effort, I decided to call Nintendo on my cell one day when I was driving and had nothing to keep me occupied. As expected, they told me I could send it in and have it fixed for something like $69 I think. BUT, the guy also asked for the model number, and when I gave it to him he said "We could also just send you a replacement (albeit refurbished) unit for $40. With $5 shipping, I got a replacement SP for $45. Sold the old one on Ebay as a "Broken" unit, and when it was all said and done my buddy essentially got a "new replacement" for $25.
I love Nintendo. The best part about it is they keep track of all the model numbers, etc. Which makes it a lot harder for any of you lurkers out there to take advantage of their generosity. At the same time, guys like my friend who really need a solution for their kids get one at a reasonable cost. As everyone else has said - I suggest calling Nintendo and asking what they can do for you.